Hi there,
We've flown with our daughter from Europe (where we're living) to the East and West Coasts twice a year since she was 3 months old, 9 and about 15 hour flights, with layovers. She's 2 now and we're packing up for another 9 hour flight this weekend!
My advice is to just remain calm and try to make it an exciting adventure for your kids. Our daughter is always so fascinated with all of the people on the plane, the arm rests going up and down, looking out the window, etc. that she never got too fussy.
Also, don't waste your energy worrying about bothering other people. If you just focus on keeping your kids happy and being patient with them, they will be happy and not be a bother to anyone. If you worry about other passengers, then they will not be getting your attention and might act up. (hope that makes sense!)
We also always bring the Byron Barton "Planes" book with us and read it while we're taking off and landing, asking her who is Mommy, Daddy, etc. in the photos.
You'll all do fine! Enjoy your trip!
H.
p.s. The last time we flew our daughter suddenly had a fever on the plane and threw up all over me in the airport... not fun, but we were all laughing about it the next day. So, if even if things do go wrong it will all be over in a few hours! :)